Partitioning Shapes into Equal Areas

3rd Grade MathGeometry4 pages

About this worksheet

A partitioning worksheet for 3rd grade dedicated entirely to Common Core 3.G.2. Nine questions move from reading to drawing to reasoning: name the unit fractions for a quartered circle, a rectangle in 3 strips, a diagonally halved square, and a hexagon in 6 triangles; draw partitions into 2, 4, 3, and 8 equal parts on shapes with printed tick-mark guides; then judge two rectangles that both show 4 parts, only one of which earns the label 1/4. The key describes an accepted drawing for every partition.

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$Partitioning Shapes into Equal Areas: Geometry - page 1$

$Partitioning Shapes into Equal Areas: Geometry - page 2$

$Partitioning Shapes into Equal Areas: Geometry - page 3$

$Partitioning Shapes into Equal Areas: Geometry - page 4$

Curriculum objectives covered

3.G.2

“Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.”

All nine questions: naming unit fractions down to 1/6 in Part 1, producing equal-area partitions up to eighths in Part 2, and the equal-versus-unequal judgment on the two rectangles in question 9.

What's inside this worksheet

Part 1: Name the Equal Parts and Unit Fractions

Four shaded figures each need two answers, the count of equal parts and the unit fraction: a circle in quadrants (1/4), a rectangle in vertical strips (1/3), a square halved by one diagonal (1/2), and a hexagon in center-point triangles (1/6).

Part 2: Partition the Shapes

Students draw straight lines on four blank outlines with subtle tick marks as guides: a rectangle into 2, a square into 4, a rectangle into 3, and a circle into 8, writing the fraction of one part under each.

Part 3: Reason About Equal Areas

Rectangle A shows 4 identical columns; Rectangle B shows 4 strips of visibly unequal widths. Question 9 asks which one 1/4 describes, and why.

How teachers use it

Fraction-unit bridge

Slot it between geometry and fractions. Question 9's unequal strips are the same trap as any unequal-parts fraction error, met here in a shapes context first.

Tick-mark scaffolding

Point out the printed tick marks in Part 2 before students draw. The circle-into-8 item is much fairer once they see the 8 perimeter marks waiting to be joined through the center.

Gallery critique

Post finished Part 2 squares on the board; a cross, a 2-by-2 grid, and four strips are all correct for question 6. Different-looking right answers make the equal-area point better than any lecture.

More 3rd Grade Math worksheets

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